Method and system for measuring the wavelength dispersion and nonlinear coefficient of an optical fiber, method of manufacturing optical fibers, method of measuring wavelength-dispersion distribution, method of compensating for measurement errors, and method of specifying conditions of measurement

ABSTRACT

A method of simultaneously specifying the wavelength dispersion and nonlinear coefficient of an optical fiber. Pulsed probe light and pulsed pump light are first caused to enter an optical fiber to be measured. Then, the power oscillation of the back-scattered light of the probe light or idler light generated within the optical fiber is measured. Next, the instantaneous frequency of the measured power oscillation is obtained, and the dependency of the instantaneous frequency relative to the power oscillation of the pump light in a longitudinal direction of the optical fiber is obtained. Thereafter, a rate of change in the longitudinal direction between phase-mismatching conditions and nonlinear coefficient of the optical fiber is obtained from the dependency of the instantaneous frequency. And based on the rate of change, the longitudinal wavelength-dispersion distribution and longitudinal nonlinear-coefficient distribution of the optical fiber are simultaneously specified.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional application of U.S. patent applicationSer. No. 10/832,875 filed Apr. 27, 2004, now U.S. Pat. No. 7,003,202which claims the benefit of the date of the earlier filed provisionalapplication, having U.S. Provisional Application No. 60/465,991, filedon Apr. 28, 2003, the contents of which are incorporated by referenceherein in their entirely.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and system for measuring thewavelength dispersion and nonlinear coefficient of an optical fiber, amethod of manufacturing optical fibers, a method of measuringwavelength-dispersion distribution, a method of compensating formeasurement errors, and a method specifying the measuring conditions.

2. Description of the Related Art

With the liberalization of the field of information communication andthe development of information society, there is a tendency for theamount of information to increase exponentially. By practical use oferbium-doped fiber amplifiers (EDFAs) and Raman fiber amplifiers thatdirectly amplify light, optical signals of extremely high power can beobtained in the band of wavelength 1.55 μm. This can make up for thetransmission losses in optical fibers and make repeater lesstransmission possible over thousands of kilometers. By employing such alight amplification technique, wavelength-division multiplexing (WDM)and time-division multiplexing (TDM) have been investigated. Also, inoptical repeatered systems employing optical amplifiers, nonlinearoptical effects become problems as optical signals of high power passthrough optical fibers. Nonlinear effects that arise within opticalfibers are self-phase modulation (SPM), cross-phase modulation (CPM),four-wave mixing (FWM), etc., which adversely affect transmissionquality. The magnitude of nonlinear effects is determined by thenonlinear coefficient of an optical fiber, so it is necessary to measurethe value with a high degree of accuracy. The nonlinear coefficient isexpressed by the following Equation:

$\gamma = {\frac{2\pi}{\lambda}\frac{n_{2}}{A_{eff}}}$where λ is the wavelength of light, n₂ is the nonlinear refractive indexof an optical fiber, and A_(eff) is the effective area of the opticalfiber. The nonlinear effects in optical fibers are evaluated by thevalue of γ or n₂/A_(eff).

In a method of measuring the nonlinear coefficient, it can be calculatedby causing the pulsed light from a light source to enter an opticalfiber, and measuring phase modulation from a change in a power spectralwaveform caused by self-phase modulation (see R. H. Stolen and ChinlonLin, Physical Review A, Vol. 17, No. 4, pp. 1448–1453 (1992)). Thismethod generally is called self-phase modulation method (hereinafterreferred to as SPM method).

In addition, by employing two light sources that generate two opticalsignals with different wavelengths, coupling the two optical signalsinto a beat pulse, and causing the beat pulse to enter an optical fiberto be measured, the nonlinear coefficient of the optical fiber can becalculated from a change in the light spectrum caused by SPM. Thismethod generally is called CW-SPM method.

Furthermore, by causing probe light and frequency-modulated pump lightto enter an optical fiber, detecting the probe light through delayedself-heterodyne detection, and detecting the phase of the probe lightmodulated by the pump light, the nonlinear coefficient of the opticalfiber can be calculated (see A. Wada et al., ECOC92, p. 42 (1992)). Thismethod generally is called cross-phase modulation method(hereinafterreferred to as XPM method).

In WDM communication, the most important nonlinear effect is four-wavemixing (FWM). If side bands caused by FWM overlap the wavelengths ofother signals, they will generate crosstalk among optical channels, andnoise that can limits WDM systems. FWM tends to occur in optical fiberswhose nonlinear effects are great, and it is also known thatparticularly, when an optical signal is in the vicinity of thezero-dispersion wavelength of an optical fiber, FWM can take placeeasily.

On the other hand, the suppression of FWM against wavelength dispersionin optical transmission lines conflicts with the conditions of waveformdistortion due to wavelength dispersion. To solve such a problem, therehas been proposed a dispersion compensating system in which localwavelength dispersion in an optical transmission line is not zero, butan optical fiber with positive wavelength dispersion and another opticalfiber with negative wavelength dispersion are combined so that thewavelength dispersion of the entire transmission line becomes close tozero.

In designing and constructing such a dispersion compensating system, itis necessary to design the nonlinear and dispersion properties of anoptical transmission line with a high degree of accuracy. In design, anoptimum fiber combination is often obtained from the average wavelengthdispersion and fiber length of an optical fiber.

However, the wavelength dispersion of an optical fiber being actuallyused is not always uniform at a certain wavelength in the fiberlongitudinal direction. The prime cause is errors in manufacturingoptical fibers and cables, etc. For that reason, in high data rate andhigh spectral density transmission with strict restrictions, there arecases where a logical design does not coincide with the state oftransmission in optical fibers being practically used.

Therefore, in such a case, the wavelength-dispersion distribution in thelongitudinal direction of an optical fiber employed in a dispersioncompensating system needs to be grasped accurately and reflected indesign.

Methods of measuring the wavelength-dispersion distribution in thelongitudinal direction of an optical fiber have been studied in view ofthe circumstances mentioned above. So far, an optical time-domainreflectometer (OTDR) utilizing linear effects, a method utilizing FWM,etc., have been proposed. A description will hereinafter be given of theprinciples of the method, utilizing FWM, which measureswavelength-dispersion distribution. The most widely used measurementmethod measures the back-scattered light of idler light generated by FWMwithin an optical fiber, and calculates dispersion from the cycle of thepower variation (see Optics Letters 1996, 21, pp. 1724–1726 and JapaneseLaid-Open Patent Publication No. Hei 8-21783). This method is called anonlinear OTDR.

Normally, equations describing degenerated four-wave mixing (DFWM) arenonlinear coupled-mode Eqs. (1) to (3).

$\begin{matrix}{{\frac{\mathbb{d}E_{p}}{\mathbb{d}z} + {\frac{1}{2}\alpha\; E_{p}}} = {{\mathbb{i}\gamma}{{{( {{E_{p}}^{2} + {2{E_{s}}^{2}} + {2{E_{c}}^{2}}} )E_{p}} + {2E_{p}^{*}E_{s}E_{c}{\exp( {{\mathbb{i}\Delta\beta}\; z} )}}}}}} & (1) \\{{\frac{\mathbb{d}E_{s}}{\mathbb{d}z} + {\frac{1}{2}\alpha\; E_{s}}} = {{\mathbb{i}\gamma}{{{( {{E_{s}}^{2} + {2{E_{c}}^{2}} + {2{E_{p}}^{2}}} )E_{s}} + {E_{c}^{*}E_{p}^{2}{\exp( {{- {\mathbb{i}\Delta\beta}}\; z} )}}}}}} & (2) \\{{\frac{\mathbb{d}E_{c}}{\mathbb{d}z} + {\frac{1}{2}\alpha\; E_{c}}} = {{\mathbb{i}\gamma}{{{( {{E_{c}}^{2} + {2{E_{p}}^{2}} + {2{E_{s}}^{2}}} )E_{c}} + {E_{s}^{*}E_{p}^{2}{\exp( {{- {\mathbb{i}\Delta\beta}}\; z} )}}}}}} & (3)\end{matrix}$where p is pump light, s is probe light, c is idler light, α is thedegree of loss in an optical fiber, and γ is the nonlinear coefficientof the optical fiber (γ=(2π/λ) (n₂/A_(eff)) where λ is the wavelength oflight, n₂ is the nonlinear refractive index of the optical fiber, andA_(eff) is the effective cross section of the core of the opticalfiber). Δβ is the phase mismatching condition of a propagation constantΔβ=β_(s)+β_(c)−2β_(P)  (4)With regard to frequency, Δβ is assumed to meet the phase matchingcondition2ω_(P)=ω_(s)+ω_(c)  (5)where ω_(p), ω_(s), and ω_(c) are the angular frequencies of pump light,probe light, and idler light, respectively.

Because it is difficult to calculate the strict solutions of Eqs. (1) to(3) (nonlinear coupled-mode equations), consideration is given byemploying the following approximate solutions.

1) Transmission losses do affect as FWM occurs.

2) The effects of SPM and XPM are not considered.

In view of these, the following Equations (6) to (8) are obtained.

$\begin{matrix}{\frac{\mathbb{d}E_{p}}{\mathbb{d}z} = 0} & (6) \\{\frac{\mathbb{d}E_{s}}{\mathbb{d}z} = 0} & (7) \\{\frac{\mathbb{d}E_{c}}{\mathbb{d}z} = {{\mathbb{i}\gamma}\; E_{s}^{*}E_{p}^{2}{\exp( {{- {\mathbb{i}\Delta\beta}}\; z} )}}} & (8)\end{matrix}$where E_(p) is the electric field of pump light of wavelength λ_(p),E_(s) is the electric field of probe light of wavelength λ_(s), E_(c) isthe electric field of idler light of wavelength λ_(c), P_(p) ⁰ is thepower of input pump light of wavelength λ_(p), P_(s) ⁰ is the power ofinput probe light of wavelength λ_(s), and Δλ is the spacing between thetwo input wavelengths.

Therefore, the electric field and power of idler light at a position ofz in the longitudinal direction are given by the following Eqs. (9) and(10):

$\begin{matrix}{E_{c} = {\frac{\gamma\; E_{s}^{*}E_{p}^{2}}{\Delta\beta}\{ {1 - {\exp( {{- {\mathbb{i}\Delta\beta}}\; z} )}} \}}} & (9) \\{P_{c} = {4( \frac{\gamma^{2}P_{s}P_{p}^{2}}{{\Delta\beta}^{2}} ){\sin( \frac{{\Delta\beta}\; z}{2} )}}} & (10)\end{matrix}$

In view of transmission losses of pump light, probe light, and idlerlight, the power of the back-scattered light of idler light receivedafter the fiber distance z is expressed by the following Eq. (11):

$\begin{matrix}{{P_{c}(z)} \propto {( \frac{\lambda_{p}}{{Dc}\;{\Delta\lambda}^{2}} )^{2}( \frac{n_{2}P_{p}^{0}}{A_{eff}} )^{2}{RP}_{s}^{0}{\sin^{2}( {{\Delta\beta}\;{z/2}} )}{\exp( {{- 4}\alpha\; z} )}}} & (11)\end{matrix}$where R=Rayleigh scattering coefficient, α=loss coefficient, andD=dispersion.

The relationship between the phase mismatching condition Δβ and thedispersion D at the wavelength of pump light is expressed by thefollowing Eq. (12):

$\begin{matrix}{{\Delta\beta} = {{{- \frac{\lambda_{p}^{2}}{2\pi\; c}}{D( \lambda_{p} )}( {\omega_{c} - \omega_{p}} )^{2}} = {\frac{\lambda_{p}^{2}}{2\pi\; c}{D( \lambda_{p} )}( {\omega_{p} - \omega_{s}} )^{2}}}} & (12)\end{matrix}$Employing λ=2πc/ω, Eq. (12) can be expressed by the following Eq. (13):

$\begin{matrix}{{\Delta\beta} = {{- 2}\pi\;{{cD}( \lambda_{p} )}( \frac{\Delta\lambda}{\lambda_{p}} )^{2}}} & (13)\end{matrix}$And the dispersion D is expressed by the following Eq. (14):

$\begin{matrix}{{D( {\lambda_{p},z} )} = {\frac{2n}{c^{2}}( \frac{\lambda_{p}}{\Delta\lambda} )^{2}{f\lbrack {t = {( \frac{2n}{c} )z}} \rbrack}}} & (14)\end{matrix}$where f(t) is the instantaneous frequency of the waveform of theback-scattered light of idler light at time t.

With the high-speed operations and increase in WDM capacity in recentyears, the design of optical transmission line requires more strictcontrol. For that reason, the optical transmission line design based onthe average wavelength dispersion and nonlinear coefficient of a certainlength of fiber, being currently used, needs to consider variations inthe wavelength dispersion in the longitudinal direction of an opticalfiber. At the same time, when the nonlinear coefficient of an opticalfiber also varies in the fiber longitudinal direction, variations in thenonlinear coefficient also affect transmission pulses. For that reason,when making a design more accurately, it is necessary to measurenonlinear-coefficient distribution as well as wavelength-dispersiondistribution.

However, at present, there is no means of measuring variations in thenonlinear coefficient in the longitudinal direction of an optical fiber.Therefore, there is no possibility that actual measurement will be made.For that reason, it is unknown how the nonlinear coefficient of anoptical fiber being presently used varies and also unknown how thevariation affects optical transmission characteristics. Therefore, thereis no investigation of how variations in the nonlinear coefficient inthe longitudinal direction of an optical fiber affect the design ofoptical transmission lines and other optical transmission analyses.

However, the nonlinear coefficient of an optical fiber is a significantparameter that characterizes optical transmission characteristics, so itis vital to investigate variations in the nonlinear coefficient in thelongitudinal direction of an optical fiber. Because of this, there is astrong demand for the development of a method and system for measuringthe properties (dispersion, nonlinear effects, etc.) of optical fibersthat can contribute to the development of next-generation transmissionlines, and fiber devices that need to adjust for the wavelengthdispersion and nonlinear coefficient.

In addition, a change in the diameter of glass when being drawing intofiber form is considered to be the main cause of variations in thewavelength dispersion in the fiber longitudinal direction produced whenmanufacturing optical fibers. The refractive-index distribution of thebase material of an optical fiber to be drawn into fiber form can bemeasured by a preform analyzer, so the drawing operation is performedbased on the result of measurement so that target wavelength dispersionis obtained. However, since there is an error in the accuracy offinishing in the fiber material or a measurement error in the preformanalyzer, not a few variations will arise in the fiber longitudinaldirection. Likewise, from the viewpoint of manufacturing optical fibers,a fiber manufacturing method that is stable and good in yield rate isrequested, and a fiber-property evaluating method therefor is alsorequested.

BRIEF SUMMARY OF THE INVENTION

The present invention has been made in order to solve theabove-described problems. Accordingly, the primary object of theinvention is to make it possible to measure the wavelength-dispersiondistribution and nonlinear-coefficient distribution in the longitudinaldirection of an optical fiber to be measured, by making use of nonlinearoptical effects that occur in the optical fiber.

To achieve this end and in accordance with a first aspect of the presentinvention, there is provided a measurement method including a step ofgenerating pulsed probe light linearly polarized, and pulsed pump lightthat is different in wavelength from the probe light but has the samepolarization state; a step of causing the probe light and the pump lightto enter an optical fiber to be measured; and a step of measuring poweroscillation of back-scattered light of the probe light caused byRayleigh scattering, or power oscillation of back-scattered light ofidler light caused by nonlinear effects generated within the opticalfiber. The measurement method further includes a step of obtaining aninstantaneous frequency of the measured power oscillation; a step ofobtaining dependency of the instantaneous frequency relative to thepower oscillation of the pump light in a longitudinal direction of theoptical fiber; a step obtaining a rate of change in the longitudinaldirection between phase-mismatching conditions and nonlinear coefficientof the optical fiber, from the dependency of the instantaneousfrequency; and a step of simultaneously specifying distributions in thelongitudinal direction of the wavelength dispersion and nonlinearcoefficient of the optical fiber, based on the rate of change.

In the measurement method of the present invention, a discriminationbetween the positive and negative of the wavelength dispersion in thelongitudinal direction of the optical fiber may be made by employingconditions on wavelengths and powers of the pulsed pump light and pulsedprobe light that are input to the optical fiber.

In the measurement method of the present invention, average wavelengthdispersion and average nonlinear coefficient of the entire optical fibermay be simultaneously specified by measuring an average value of thepower oscillation of the idler light at a pulse exit side of the opticalfiber, measuring dependency of the conversion efficiency of the idlerlight relative to the power oscillation of input pulsed pump light onthe basis of the measure average value, and performing a regressionanalysis of the conversion efficiency with a logic function representingthe conversion efficiency of the idler light dependent on the poweroscillation of the pump light on the basis of the measured dependency.

In the measurement method of the present invention, influence ofvariations in polarization within the optical fiber may be removed bymeasuring longitudinal wavelength-dispersion distribution andlongitudinal nonlinear-coefficient distribution at both ends of theoptical fiber and comparing the measured two distributions.

In the measurement method of the present invention, predeterminedamounts of data near both ends of the optical fiber may be deleted fromthe power oscillation data of the idler light or pulsed probe light. Andthe power oscillation data after the deletion may be analyzed.

In accordance with a second aspect of the present invention, there isprovided a measurement system including a pump light source forgenerating pump light; a probe light source for generating probe light;and a modulator for pulsing the pump light and/or the probe light. Themeasurement system further includes a first coupler, light-receivingmeans, and calculation means. The first coupler is used for coupling thepulsed pump light and the pulsed probe light together and inputting themto an optical fiber to be measured. The light-receiving means is usedfor wavelength-selecting either back-scattered light of the pulsed probelight occurring within the optical fiber or back-scattered light of thepulsed idler light occurring within the optical fiber, after the pulsedpump light and the pulsed probe light are input to the optical fiber,and outputting an electric signal representing a waveform of theselected scattered light. The calculation means is used for calculatingwavelength-dispersion distribution and nonlinear-coefficientdistribution in a longitudinal direction of the optical fiber from awaveform of the electric signal.

The measurement system of the present invention may further includeoptical amplification means for amplifying the aforementioned pulsedpump light.

The measurement system of the present invention may further includebranch means and an acoustooptic modulator. The branch means is used forbranching the probe light generated by the probe light source into firstlight and second light. The acoustooptic modulator is used forfrequency-shifting the probe light by pulsing the first light. Theaforementioned light-receiving means may have a second coupler thatcouples back-scattered light of the pulsed probe light output from theacoustooptic modulator, and the second light branched by the branchmeans.

The measurement system of the present invention may further includeRaman amplification means, which is used for causing idler lightdifferent in wavelength from the pump light and probe light to entereither end or both ends of the optical fiber, and Raman-amplifying thepulsed pump light, the pulsed probe light, and the idler light.

The measurement system of the present invention may further include apower measuring unit, disposed on a pulse exit side of the opticalfiber, for measuring power oscillation of idler light.

The measurement system of the present invention may further include anonlinear optical medium provided between the first coupler and theoptical fiber.

In the measurement system of the present invention, the aforementionedpump light source and the aforementioned probe light source may generatepump light and probe light that have linear polarizations parallel toeach other. And the aforementioned first coupler may couple the pumplight and the probe light so that their polarization planes coincidewith each other.

In the measurement system of the present invention, the aforementionedpump light source and the aforementioned probe light source may generatepump light and probe light that have linear polarizations parallel toeach other. The aforementioned first coupler may couple the pump lightand the probe light so that their polarization planes coincide with eachother. And the aforementioned second coupler may couple back-scatteredlight of the probe light, back-scattered light of the pulsed probe lightoutput from the acoustooptic modulator, and the second light branched bythe branch means so that their polarization states are parallel to oneanother.

In accordance with a third aspect of the present invention, there isprovided a method comprising the steps of: measuringwavelength-dispersion distribution and nonlinear-coefficientdistribution in a longitudinal direction of an optical fiber drawn intofiber form, by employing the measurement system as set forth in any oneof claims 6 to 13; and cutting off the optical fiber so that either themeasured wavelength-dispersion distribution or the measurednonlinear-coefficient distribution, or both are within ±5% of an averagevalue of the entire length of the optical fiber.

In accordance with a fourth aspect of the present invention, there isprovided a method of measuring wavelength-dispersion distribution in alongitudinal direction of an optical fiber to be measured. The methodcomprises the steps of extracting waveform data of an optical signalpropagating within the optical fiber for each of a plurality of regions;nonlinearly fitting the waveform data extracted for the regions to asinusoidal function; respectively calculating dispersions of thewaveform data extracted for the regions; and measuring thewavelength-dispersion distribution.

In accordance with a fifth aspect of the present invention, there isprovided a method of compensating for a measurement error that occurs inmeasuring wavelength-dispersion distribution in a longitudinal directionof an optical fiber to be measured. The method includes the step ofcompensating for the measurement error by employing oscillation power ofinput pump light, oscillation power of input signal light, conditions ofmeasuring spacing between the input pump light and the input signallight, a nonlinear coefficient of the optical fiber, and oscillationpower of idler light of a measuring object.

In accordance with a sixth aspect of the present invention, there isprovided a method of specifying measuring conditions that are set inmeasuring wavelength-dispersion distribution in a longitudinal directionof an optical fiber to be measured. The method includes the step ofspecifying the measuring conditions, based on wavelength dispersion andnonlinear coefficient of the optical fiber.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described in further detail with referenceto the accompanying drawings wherein:

FIG. 1 is a block diagram showing a measurement system constructed inaccordance with a first embodiment of the present invention;

FIG. 2 is a block diagram showing a measurement system constructed inaccordance with a second embodiment of the present invention;

FIG. 3 is a block diagram showing a measurement system constructed inaccordance with a third embodiment of the present invention;

FIG. 4 is a block diagram showing a measurement system constructed inaccordance with a fourth embodiment of the present invention;

FIG. 5 is a block diagram showing a measurement system constructed inaccordance with a fifth embodiment of the present invention;

FIG. 6 is a block diagram showing a measurement system with apolarization holding function, constructed in accordance with a sixthembodiment of the present invention;

FIG. 7 is a block diagram showing a measurement system with apolarization holding function employing an optical heterodyne detectionmethod, constructed in accordance with a seventh embodiment of thepresent invention;

FIG. 8 is a diagram showing the measurable region in a reverseddispersion fiber;

FIG. 9 is a diagram showing the measurable region in a high nonlinearityfiber;

FIG. 10 is a diagram showing the waveforms of the back-scattered lightof idler light measured when the power of input pump light is varied;

FIG. 11 is a diagram showing the wavelength-dispersion distribution inthe longitudinal direction of a fiber obtained by the result ofanalyses;

FIG. 12 is a diagram showing the nonlinear-coefficient distribution inthe fiber longitudinal direction obtained by the result of analyses;

FIG. 13 is a flowchart used to explain the steps in an optical-fibermanufacturing method employed in the embodiments of the presentinvention;

FIG. 14 is a diagram showing the waveform measured by an opticaltime-domain reflectometer (OTDR); and

FIG. 15 is a diagram showing dispersion distribution calculated by adirect fitting method.

DETAILED DESCRIPTION OF THE INVENTION

Initially, a description will be given of the principles of a methodthat measures the longitudinal nonlinear-coefficient distribution andwavelength-dispersion distribution of an optical fiber when four-wavemixing occurs in the optical fiber.

In conventional methods that measure the longitudinalwavelength-dispersion distribution of an optical fiber, the influence ofnonlinear effects such as self-phase modulation and cross-phasemodulation is not considered. In embodiments of the present invention, ameasuring system for producing these nonlinear effects is constructed inorder to calculate the nonlinear coefficient of an optical fiber. Also,the influence of nonlinear effects in the measuring system is measuredin the fiber longitudinal direction. Based on the result of measurement,the longitudinal wavelength-dispersion distribution andnonlinear-coefficient distribution of the optical fiber aresimultaneously measured. Now, a description will be given of thesolution derived by Stolen and Bjorkholm (hereinafter referred to as SBsolution) when the nonlinear effects on probe light and idler light bythe self-phase modulation and cross-phase modulation caused by pumplight are not negligible. The SB solution is characterized in that itcontains nonlinear effects, such as self-phase modulation andcross-phase modulation, caused by pump light. And this SB solution isestablished when the power of pump light is extremely high. However,this SB solution does not take the transmission losses in optical fibersinto consideration. The basic equations for the SB solution are given bythe following Eqs. (15) to (17):

$\begin{matrix}{\frac{\mathbb{d}E_{p}}{\mathbb{d}z} = {{\mathbb{i}\gamma}{E_{p}}^{2}E_{p}}} & (15) \\{\frac{\mathbb{d}E_{s}}{\mathbb{d}z} = {{\mathbb{i}\gamma}\lbrack {{2{E_{p}}^{2}E_{s}} + {E_{C}^{*}E_{p}^{2}{\exp( {{- {\Delta\beta}}\; z} )}}} \rbrack}} & (16) \\{\frac{\mathbb{d}E_{c}}{\mathbb{d}z} = {{\mathbb{i}\gamma}\lbrack {{2{E_{p}}^{2}E_{c}} + {E_{s}^{*}E_{p}^{2}{\exp( {{- {\Delta\beta}}\; z} )}}} \rbrack}} & (17)\end{matrix}$Also, the power P_(c)(z) of idler light and power P_(s)(z) of probelight after a distance of z are expressed as follows:Case A: When Δβ<0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4γ,

$\begin{matrix}{{{Idler}\mspace{14mu}{light}\mspace{14mu}{P_{c}(z)}} = {\frac{4\gamma^{2}P_{p}^{02}P_{s}^{0}}{- {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}^{0}}} )}}{\sinh^{2}( {g_{a}z} )}}} & (18) \\{{{{Probe}\mspace{14mu}{light}\mspace{14mu}{P_{S}(z)}} = {P_{S}^{0}( {1 - {\frac{4\gamma^{2}P_{P}^{0^{2}}}{{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{P}^{0}}} )}{\sinh^{2}( {g_{a}z} )}}} )}}{where}} & (19) \\{g_{a} = {\frac{1}{2}\lbrack {- {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}}} )}} \rbrack}^{1/2}} & (20)\end{matrix}$P_(s) ⁰ represents the power of incident probe light, and P_(p) ⁰represents the power of incident pump light.Case B: When Δβ<0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4γ, or whenΔβ≧0 (normal dispersion),

$\begin{matrix}{{{Idler}\mspace{14mu}{light}\mspace{14mu}{P_{c}(z)}} = {\frac{4\gamma^{2}P_{p}^{02}P_{s}^{0}}{{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}^{0}}} )}{\sin^{2}( {g_{b}z} )}}} & (21) \\{{{{Probe}\mspace{14mu}{light}\mspace{14mu}{P_{S}(z)}} = {P_{S}^{0}( {1 + {\frac{4\gamma^{2}P_{P}^{0^{2}}}{{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{P}^{0}}} )}{\sin^{2}( {g_{b}z} )}}} )}}{where}} & (22) \\{g_{b} = {\frac{1}{2}\lbrack {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}}} )} \rbrack}^{1/2}} & (23)\end{matrix}$

From Eqs. (18), (19) and (21), (22) it is found that the powers P_(c)(z)and P_(s)(z) of idler light and probe light that propagate in the fiberlongitudinal direction vary in dependence on Δβ, γ, and the power P_(p)of pump light. Hence, as in the case where Mollenaure et al. payattention to g_(a) and g_(b) Of the back-scattered light of idler lightin Eq. (11) and calculate Δβ from g_(a) and g_(b), if in Eqs. (18), (19)and Eqs. (21), (22) the power of the back-scattered light of idler lightor probe light is measured and g_(a) and g_(b) after a distance of z arecalculated, information on the dispersion or nonlinear coefficient isobtained from g_(a) and g_(b).

As set forth above, in the above-described SB solution, transmissionlosses in optical fibers are not considered. Because g_(a) and g_(b) ofthe probe light or idler light depend on the power of pump light,transmission losses g_(a) and g_(b) will vary. For that reason, whencalculating Δβ and γ accurately, transmission losses must be considered.There are two methods of taking the effect of transmission losses intoEqs. (18) to (23).

Case C:

The power of pump light at points in the fiber longitudinal direction iscalculated from the power of input pump light and fiber loss coefficientd. And by employing these values, g_(a) and g_(b) are calculated. In theabove-described two cases,

(C1) When Δβ<0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4γ,

$\begin{matrix}{g_{a} = {\frac{1}{2}\lbrack {- {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}{\exp( {{- \alpha}\; z} )}}} )}} \rbrack}^{1/2}} & (24)\end{matrix}$

(C2) When Δβ<0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4 γ, or when Δβ≧0(normal dispersion),

$\begin{matrix}{g_{b} = {\frac{1}{2}\lbrack {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}{\exp( {{- \alpha}\; z} )}}} )} \rbrack}^{1/2}} & (25)\end{matrix}$Case D:

The power P_(p)(z) of pump light at points in the fiber longitudinaldirection is actually measured by measuring the back-scattered light ofpump light. And by employing these values, g_(a) and g_(b) arecalculated. As with the case C,

(D1) When Δβ<0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4γ,

$\begin{matrix}{g_{a} = {\frac{1}{2}\lbrack {- {{\Delta\beta}( {{\Delta\beta} + {4\gamma\;{P_{p}(\; z)}}} )}} \rbrack}^{1/2}} & (26)\end{matrix}$

(D2) When Δβ≦0 (anomalous dispersion) and P_(p) ⁰>−Δβ/4 γ, or when Δβ≧0(normal dispersion),

$\begin{matrix}{g_{b} = {\frac{1}{2}\lbrack {{\Delta\beta}( {{\Delta\beta} + {4\gamma\;{P_{p}(\; z)}}} )} \rbrack}^{1/2}} & (27)\end{matrix}$

In the case of optical fibers where the fiber loss coefficient d isgreat, or in the case of optical fibers where the fiber length is longand therefore the total loss is great, it is effective to amplify pumplight, probe light, and idler light by forward Raman amplification andbackward Raman amplification. In such a case, variations in the power inthe longitudinal direction of pump light are not a reducingcharacteristic proportional to the fiber loss coefficient. Therefore, itbecomes effective to employ actual measurements, as in the case D.

Two solutions of Eqs. (18), (19) and Eqs. (21), (22) are obtained fromthe conditions of Δβand P_(p), but either solution may be employed.However, for the evaluation of wavelength dispersion, Eqs. (21) and (22)are effective. The reason for that is that the dependency of g_(b)relative to the power oscillation of pump light varies between the caseof anomalous dispersion (Δβ<0) and the case of normal dispersion (Δβ≧0).That is, depending on the positive or negative of Δβ, a variation ing_(b) at the time of an increase in the pump light power decreases inthe case of abnormal dispersion (Δβ<0) and increases in the case ofnormal dispersion (Δβ≧0). Therefore, by measuring an increase ordecrease in g_(b) relative to the power oscillation of pump light, itbecomes possible to discriminate between the positive and negative ofthe wavelength dispersion of an optical fiber. This advantage isunobtainable in the existing methods of measurement.

Referring now to FIG. 1, there is shown a measurement system 100constructed in accordance with a first embodiment of the presentinvention. The measurement system 100 is used for simultaneouslymeasuring the wavelength-dispersion distribution and nonlinearcoeffcient distribution in the longitudinal direction of an opticalfiber to be measured.

Light from a pump light source 1 is phase-modulated by a phase modulator2. A sinusoidal wave signal with a frequency of 100 MHz or so, outputfrom a sine-wave generator 3, is input to the phase modulator 2 throughan electric signal amplifier 4. The phase modulation is performed inorder to prevent stimulated Brillouin scattering (SBS) from taking placewithin an optical fiber 5 to be measured (hereinafter referred to simplyas an optical fiber 5). In the case where the power of the pump lightincident on the optical fiber 5 is less than or equal to a SBSthreshold, phase modulation is not necessary. The signal from the phasemodulator 2 is pulsed by a power modulator 6. The cycle f of the pulseapplied to the power modulator 6 is determined by the time the pulsetakes to go and return the fiber length of the optical fiber 5 and isrepresented as f=c/2nL (where L is the fiber length and n is therefractive index of the fiber). The duty ratio of the pulse is about afew %. The pulsed light from the power modulator 6 is amplified by anerbium-doped fiber amplifier (EDFA) 7. The amplified pump light passesthrough a band-pass filter 8 and a polarization controller 9 and entersa coupler 10. On the other hand, the probe light generated by a probelight source 11 is pulsed by a power modulator 12 in the same manner asthe aforementioned pump light and is coupled with the pump light by thecoupler 10. At this time, the pump light passes through a delay line 13and a polarization controller 14 in order to cause the two pulses (ofthe pump light and probe light) to coincide with each other in timingand state of polarization. The coupled light passes through a circulator15 and enters the optical fiber 5. The terminal of the optical fiber 5is connected to a reflection less end 16. The back-scattered light ofthe probe light or idler light from the optical fiber 5 passes throughthe circulator 15, optical filter 17, EDFA 18, and optical filter 19 andis converted into an electric signal by an O/E converter 20. Thiselectric signal is measured by an oscilloscope 21. A trigger signal froma pulse generator 22 is input to the oscilloscope 21. The power of thepump light and power of the probe light that enter the optical fiber 5are measured at the output port of the circulator 15 by an optical powermeter 231. The electric pulse signal required for pulsing theaforementioned pump light and probe light is generated by the pulsegenerator 22 and is branched into two. The two branched signals areamplified by electric signal amplifiers 23 and 24 a, respectively. Theyare further synthesized with DC voltage components output from DC powersources 25, 26 and are respectively input to the power modulators 12, 6.The electric signal input to the oscilloscope 21 is digitized, and it isinput to a computer 24.

Note that the pump light wavelength λp, its input power, and probe lightwavelength λs are suitably set in dependence on the properties of theoptical fiber 5 important for communications. The details of thewavelength setting will be described below, but the reason why thewavelength setting is required is that the above-described conditions ofmeasurement and conditions of analysis (conditions of SB solutions) mustbe met.

Now, steps of measurement by the measurement system 100 will bedescribed. A description will be given of an analysis method employingEqs. (21), (22), and (23) by which information on the positive andnegative of wavelength dispersion is obtained. A vital point in themeasurement is that measuring conditions meeting the above-describedconditional Equations are set in dependence on the wavelength dispersionand nonlinear coefficient of the optical fiber 5. In setting suchmeasuring conditions, it is also necessary that they be within thecapability range of the measurement system 100 that is practically used.

Initially, the flow from the setting of measuring conditions to thefinal calculation of analyzed data will hereinafter be described.

Measurement 1: Set measuring conditions (see the following) inconsideration of the characteristics of the optical fiber 5 andmeasurement system 100.

Measurement 2: Measure the back-scattered light of pump light with themeasurement system 100 and acquire the power in the fiber longitudinaldirection of the pump light.

Measurement 3: Measure the waveform of the back-scattered light of probelight or waveform of the back-scattered light of idler light with themeasurement system 100.

Measurement 4: Change the power of input pump light a plurality of timesand repeat the steps of the measurements 2 and 3

Measurement 5: Calculate g_(b) at each point in the fiber longitudinaldirection from the waveform of the probe light or idler light with themeasurement system 100.

And by substituting into Eq. (27) a plurality of g_(b) values relativeto the power of pump light at points in the fiber longitudinal directionobtained in the above-described Measurement 5, Δβ and γ are calculated.

Next, a detailed description will be given of the aforementionedmeasurement 1.

The setting of measuring conditions varies greatly, depending on theproperties of an optical fiber important for light transmission. Hence,first consider the setting of measuring conditions in dependence on thetype of optical fiber 5 being used.

The setting of measuring conditions is performed on the assumption thatthe values of the fiber length, average dispersion, and nonlinearcoefficient (per fiber length) of the optical fiber 5 are known. Theapproximate values of the nonlinear coefficient and average wavelengthdispersion are typically known, depending on the types of optical fibersbeing used. Therefore, the minimum information required for the settingof measuring conditions is what the type of optical fiber 5 is, and isthe value of the fiber length of the optical fiber 5. As an example,typical types of 1.55-μm-band single mode fibers, the wavelengthdispersions, and the nonlinear coefficients are listed in Table 1.

TABLE 1 Nonlinear Dispersion coefficient Fiber Type D(ps/nm/Km) γ(km⁻¹W⁻¹) DCF(dispersion-compensated fiber) −150 to −80 10.9RDF(reversed dispersion fiber) −17 4.9 SMF(single mode fiber) +17 1.2DSF(dispersion-shifted fiber) −2 to +2 2.0 NZ-DSF(non-zero −4 to −2, 2.0dispersion-shifted fiber) +2 to +4 HNLF(high nonlinearity fiber) −4 to+4 20.0

The measuring conditions vary, depending on whether Δβ is positive ornegative (whether wavelength dispersion is normal or anomalous). Hence,steps 1 to 3 of setting the measuring conditions will be described independence on the positive and negative of Δβ.

Condition-setting step 1 in the case of anomalous wavelength dispersion(Δβ<0):

1-1. Setting of Distance Resolution:

Set the frequency per 1 km of a measured waveform (frequency=number ofwaves: g_(b) (km⁻¹)/π) to 2 to 10 (when P_(p)=0 W)

Since Δβ=−2 g_(b) when P_(p)=0 W,

Δβ(km⁻¹)=−4πto −20π(≡Δβmax)

1-2. Setting of the Upper Limit Value of Input Pump Light Power:

Calculate power P_(pmax) meeting the critical condition of pump lightfrom the nonlinear coefficient γ.P _(pmax)=−Δβmax/4γ

Compare P_(pmax) with the upper limit value P_(pmeasure) Of themeasurement system.

-   -   a) P_(pmeasure)≦P_(pmax)−>Set upper limit value        -   P_(phigh)=P_(pmeasure)    -   b) P_(pmeasure)>P_(pmax)−>Set upper limit value        -   P_(phigh)=P_(pmax)

1-3. Determination of Δβ:

Calculate the spacing Δλ between the two wavelengths of pump light andprobe light with respect to Δβ calculated in the above-described 1-1,using Eq. (13).

a) Δλ≦Δλ_(max) (measurement system limit)−>Determination of Δλ

b) Δλ>Δλ_(max)−>Δλ=Δλ_(max) (a new Δβ is determined)

1-4. Determination of an Input Pump Light Power Variable Region:

Determine a pump light region where the wave amplitude component A ofprobe light or idler light (A=4γ²P_(p) ²/{Δβ(Δβ+4 γP_(p))}) is ameasurable value.

A measurable limit value A_(lim) is determined in dependence on thereceiving sensitivity of the measurement system being used. Assuming thepower of pump light is P_(pmin) when A=A_(lim), the region where thepower is variable isP _(pmin) ≦P _(p) ≦P _(phigh)

1-5. Confirmation of g_(b) in Probe Light or Idler Light to Be Measured:

Calculate g_(b) of the waveform of pump light or probe light in the pumplight region calculated in the above-described 1-4, using Eq. (23).g _(b)(P _(p) =P _(phigh))≦g _(b) ≦g _(b)(P _(p) =P _(pmin))

Condition-setting step 2 in the case of normal wavelength dispersion(Δβ>0):

2-1. Setting of Distance Resolution:

Set the frequency per 1 km of a measured waveform (frequency=number ofwaves: g_(b) (km ⁻¹)/π) to 2 to 10 (when P_(p)=0 W).Δβ=4π to 20π(≡Δβmax)

2-2. Determination of Δβ:

Calculate the spacing Δλ between the two wavelengths of pump light andprobe light from Δβ determined, using Eq. (13).

a) αλ≦Δα_(max) (measurement system limit)−>Determination of Δλ

b) Δλ>Δλ_(max)−>Δλ=Δλ_(max)

2-3. Determination of an Input Pump Light Power Variable Region:

Determine a pump light region where the wave amplitude component A ofprobe light or idler light (A=4γ²P_(p) ²/{Δβ(Δβ(Δβ+4 γP_(p))}) is ameasurable value.

A measurable limit value A_(lim) is determined in dependence on thereceiving sensitivity of the measurement system being used. If the powerof pump light is assumed to be P_(pmin) when A=A_(lim), the region wherethe power is variable isP _(pmin) ≦P _(p) ≦P _(phigh)

2-4. Confirmation of g_(b) in Probe Light or Idler Light to Be Measured:

Calculate g_(b) Of the waveform of pump light or probe light in the pumplight region calculated in the above-described 2-3, using Eq. (23).g _(b)(P _(p) =P _(pmin))≦g _(b) ≦g _(b)(P _(p) =P _(phigh))

Condition-setting step 3 in the case of optical fibers where it cannotbe judged if wavelength dispersion is positive or negative:

Particularly, in the case of optical fibers where the positive andnegative of wavelength dispersion vary in the fiber longitudinaldirection for reasons of manufacture because average wavelengthdispersion is close to zero, as in dispersion-shifted fibers, or in thecase of optical fibers where wavelength dispersion is intentionallyadjusted in the fiber longitudinal direction (e.g.,dispersion-decreasing fibers), it cannot be distinctly decidedbeforehand if wavelength dispersion is positive or negative. In such acase, as set forth below, it is considered effective to set measuringconditions on the assumption that optical fibers are anomalousdispersion fibers, and correct the set values by experiment. This isbecause the number of limiting factors becomes greater in the case ofanomalous dispersion fibers because of the presence of the criticalcondition of pump light (P_(p)(0)<−Δβ/4γ). On the other hand, thesetting of measuring conditions is not always easier in the case ofnormal dispersion fibers than in the case of anomalous dispersionfibers. In this case, in the same pump light power, a variation in thewave amplitude component of probe light and idler light is smaller andfeebler in the case of anomalous dispersion fibers than in the case ofnormal dispersion fibers where the absolute value of wavelengthdispersion is the same but different in sign. For that reason, bycorrecting the value of Δβ(Δλ) in a reducing direction from conditionsobtained on the assumption that optical fibers are anomalous dispersionfibers, and by making the wave amplitude components of probe light andidler light greater, it becomes necessary to broaden a measurableregion. A description will hereinafter be given of themeasuring-condition setting steps in the case of optical fibers where itcannot be judged if wavelength dispersion is positive or negative.

3-1. Setting of Distance Resolution:

Set the frequency per 1 km of a measured waveform (frequency=number ofwaves: g_(b)(km⁻¹)/π) to 2 to 10 (when P_(p)=0 W).Δβ=4π to 20π(≡Δβmax)

3-2. Setting of the Upper Limit Value of Input Pump Light Power:

Calculate power P_(pmax) meeting the critical condition of pump lightfrom the nonlinear coefficient γ.P _(pmax)=−Δβ_(max)/4γ

Compare P_(pmax) with the upper limit value P_(pmeasure) of themeasurement system.

-   -   a) P_(pmeasure)≦P_(pmax)−>Set upper limit value        -   P_(phigh)=P_(pmeasure)    -   b) P_(pmeasure)>P_(pmax)−>Set upper limit value        -   P_(phigh)=P_(pmax)

3-3. Determination of Δβ:

Calculate the spacing Δλ between the two wavelengths of pump light andprobe light with respect to Δβ calculated in the above-described 3-1,using Eq. (13).

a) Δλ≦Δλ_(max) (measurement system limit)−>Determination of Δλ

b) Δλ>Δλ_(max)−>Δλ=Δλ_(max) (a new Δβ is determined)

3-4. Determination of an Input Pump Light Power Variable Region:

Determine a pump light region where the wave amplitude component A ofprobe light or idler light (A=4γ²P_(p)/{Δβ(Δβ+4 γP_(p))}) is ameasurable value.

A measurable limit value A_(lim) is determined in dependence on thereceiving sensitivity of the measurement system being used. Assuming thepower of pump light is P_(pmin) when A=A_(lim), the region where thepower is variable isP _(pmin) ≦P _(p) ≦P _(phigh)

3-5. Confirmation of g_(b) in Probe Light or Idler Light to Be Measured:

Calculate g_(b) of the waveform of pump light or probe light in the pumplight region calculated in the above-described 3-3, using Eq. (23).Anomalous dispersion: g _(b)(P _(p) =P _(phigh))≦g _(b) ≦g _(b)(P _(p)=P _(pmin))Normal dispersion: g _(b)(P _(p) =P _(pmin))≦g _(b) ≦g _(b)(P _(p) =P_(phigh))

With the measuring-condition setting steps 1 to 3, measuring conditionsare set for the optical fiber 5. The results are listed in Tables 2 and3. Also, in FIGS. 8 and 9, there are shown measurable regions for areversed dispersion fiber (RDF) with dispersion of −17 ps/nm/km and ahigh nonlinearity fiber (HNLF) with dispersion of 4 ps/nm/km. Thereceiving sensitivity of the measurement system 100 is A_(lim)=0.1.Since A_(lim) is determined in dependence on the system characteristicsof the measurement system 100, the above-described measuring conditionsare not to be taken as limiting the present invention.

TABLE 2 Number of Fiber D γ Δ β Δ λ P_(p)(W) g_(b) waves measured type(ps/nm/km) (km⁻¹W⁻¹) (km⁻¹) (nm) region region (km⁻¹) SMF 17 1.2 −30.31.512 3~6 10.98~3.37 1.74~0.54 DSF 2 2.0 −50.5 5.691 3~6 18.29~5.622.91~0.89 1 2.0 −50.5 8.049 3~6 18.29~5.62 2.91~0.89 0.1 2.0 −48.7 252.9~6   17.62~2.92 2.80~0.46 NZ-DSF 4 2.0 −50.5 4.024 3~6 18.29~5.622.91~0.89 3 2.0 −50.5 4.647 3~6 18.29~5.62 2.91~0.89 HNLF 4 20 −125.66.347 0.75~1.5   57.6~13.26 9.15~2.16 3 20 −125.6 7.328 0.75~1.5  57.6~13.26 9.15~2.16 2 20 −125.6 8.976 0.75~1.5   57.6~13.26 9.15~2.161 20 −125.6 12.693 0.75~1.5   57.6~13.26 9.15~2.16 0.1 20 −48.7 250.30~0.60 17.34~2.92 2.76~0.46

TABLE 3 Number of Fiber D γ Δ β Δ λ P_(p)(W) g_(b) waves measured type(ps/nm/km) (km⁻¹W⁻¹) (km⁻¹) (nm) region region (km⁻¹) DCF −150 10.9125.6 1.036 2.5~6.3 85.83~112.11 13.66~17.84 −120 10.9 125.6 1.1592.5~6.3 85.83~112.11 13.66~17.84 −100 10.9 125.6 1.269 2.5~6.385.83~112.11 13.66~17.84 −80 10.9 125.6 1.419 2.5~6.3 85.83~112.1113.66~17.84 RDF −17 4.9 61.74 2.158 1.4~6.3 42.43~53.47  6.75~8.51 DSF−4 2.0 25.2 2.843 2.8~6.3 17.32~21.82  2.76~3.47 −3 2.0 25.2 3.2832.8~6.3 17.32~21.82  2.76~3.47 −2 2.0 25.2 4.020 2.8~6.3 17.32~21.82 2.76~3.47 −1 2.0 25.2 5.686 2.8~6.3 17.32~21.82  2.76~3.47 −0.1 2.024.35 17.674 2.7~6.3 16.73~21.33  2.66~3.39 HNLF −4 20.0 125.6 6.3471.4~6.3 86.38~140.60 13.75~22.38 −3 20.0 125.6 7.328 1.4~6.386.38~140.60 13.75~22.38 −2 20.0 125.6 8.976 1.4~6.3 86.38~140.6013.75~22.38 −1 20.0 125.6 12.693 1.4~6.3 86.38~140.60 13.75~22.38 −0.120.0 48.7 25 3.0~6.3 59.29~82.03   9.44~13.06

The effects of stimulated Brillouin scattering (SBS) must be consideredin setting the maximum input power of pump light. If SBS occurs, thepower of light passing through an optical fiber is limited even if theinput power of pump light is increased, and it is difficult toaccurately measure the power dependency of pump light. Because of this,the input power needs to be set to less than a SBS threshold for opticalfibers. The SBS threshold varies depending on the optical properties ofthe optical fiber 5 (nonlinear effects, etc.) and fiber length, so it isnecessary to previously confirm that SBS has not occurred in the opticalfiber 5, when making a measurement. To raise the SBS threshold andenlarge the input power of pump light, it is also effective to broadenthe spectral linewidth by phase modulation, etc.

After the above-described measurements 1 to 4, the values of g_(b) atpoints in the longitudinal direction of the optical fiber 5 arecalculated from the power and waveform of back-scattered light of probelight or idler light obtained (measurement 5), and Δβ and γ arecalculated from the calculated values of g_(b) and the pump light power.

Initially, calculate g_(b). The g_(b) of a sinusoidal waveform can becalculated by the same method as the method disclosed by L. F.Mollenauer et al. In this method, measured data is first passed througha band-pass filter to remove a frequency component other than a signalfrequency component. Then, by performing fast Fourier transform (FFT),the negative frequency is replaced with zero. Next, by performinginverse fast Fourier transform (IFFT), the imaginary component of themeasured data is calculated. Thereafter, phase angles at points in thefiber longitudinal direction are calculated from the real component andimaginary component. These phase angles are values corresponding tog_(b). In this way, the values Of g_(b) at points in the fiberlongitudinal direction with respect to input pump light power areobtained.

Next, calculate Δβ and γ from the calculated values Of g_(b). First, thevalues of 4g_(b) ² are plotted with respect to the pump light power atpoints in the fiber longitudinal direction. By performing a fittingoperation on these plots by using a straight line, the intercept andslope are found. As indicated in Eq. (23), that intercept representsΔβ². At this time, if the slope of that straight line is positive, thedispersion in the optical fiber 5 at that point is normal dispersion.Conversely, in the case of negative, it is anomalous dispersion. And theabsolute value of that slope is 4Δβγ, so γ can be obtained from thevalue of Δβ obtained from the aforementioned slope. Therefore, byperforming this manipulation over the entire region in the longitudinaldirection, it can be found how the wavelength dispersion, the positiveand negative, and the nonlinear coefficient are distributed in thelongitudinal direction.

In addition, for the waveform of the back-scattered light of each ofpump light, probe light, and idler light to be measured, there are caseswhere at the connection parts of both ends of an optical fiber to bemeasured, reflection takes places and a peak occurs. Furthermore, thereis a possibility that the waveform distortion of the rising part of awaveform on the side of incidence will cause errors during FFT analysis.Therefore, by removing predetermined portions of both ends of theobtained waveform and then making calculations, a total calculationerror can be suppressed.

FIG. 10 shows the waveforms of the back-scattered light of idler lightmeasured when the power of pump light to be input to a high nonlinearityfiber is varied. Also, FIG. 11 shows the wavelength-dispersiondistribution in the longitudinal direction of a fiber obtained from thevalues shown in FIG. 10 by the above-described analysis method. FIG. 12shows the nonlinear-coefficient distribution in the fiber longitudinaldirection obtained from the values shown in FIG. 10 by theabove-described analysis method.

With reference to FIG. 13, a description will be given of a method ofmanufacturing optical fibers, based on a method of measuring thewavelength dispersion and nonlinear coefficient in the longitudinaldirection of an optical fiber by employing the above-describedmeasurement system 100.

Initially, the base material of an optical fiber is prepared (step S1)and the distribution of refractive indexes of the base material ismeasured with a preform analyzer (step S2). Based on the result ofmeasurement, fiber-drawing conditions (linear tensile strength, speed,temperature of a molten portion, etc.) are determined (step S3). Thebase material is drawn into fiber form, and for the obtained opticalfiber, the wavelength-dispersion distribution and nonlinear-coefficientdistribution in the fiber longitudinal direction are measured with theabove-described measurement system 100. In dependence on the result ofevaluation, a portion of the fiber is cut off so that the longitudinalnonlinear-coefficient distribution and/or longitudinalwavelength-dispersion distribution are within a variation of ±5% withrespect to an average value over the entire fiber length (step S5).Thus, in this embodiment, by measuring the wavelength dispersion andnonlinear coefficient in the longitudinal direction of an optical fiber,and cutting off a portion of the fiber so that the nonlinear coefficientand wavelength dispersion are optimum, optical fibers are manufacturedwhich have uniform and stable wavelength dispersion and nonlinearcoefficient, compared with conventional fibers (step S6).

Thus, according to the measurement system 100 of the first embodiment,the longitudinal nonlinear-coefficient distribution andwavelength-dispersion distribution of an optical fiber can be measuredat the same time. In addition, proper methods of analysis are employedfor 1.55-μm-band fibers having various types of wavelength dispersion,so the measurement system 100 is also applicable to optical fibers withvarious types of wavelength dispersion. Furthermore, by employing theabove-described measurement method in the fiber-manufacturing process,optical fibers are obtained in which the properties are uniform andstable in the fiber longitudinal direction. Therefore, these opticalfibers make a great contribution in designing dispersion-compensatinglines and soliton-communication lines that are employed repeaterlesslong-distance transmission of strong light power employing erbium-dopedfiber amplifiers, so the utilization value is great.

Instead of using the measurement system 100, other measurement systemsmay be used for measuring the wavelength-dispersion distribution andnonlinear-coefficient distribution in the longitudinal direction of theoptical fiber 5. Measurement systems other than the measurement system100 will hereinafter be described with reference to FIGS. 2 to 7.

Referring to FIG. 2, there is shown a measurement system 101 constructedin accordance with a second embodiment of the present invention. Themeasurement system 101 is constructed to receive probe light byemploying an optical heterodyne detection method in order to enhance thesensitivity of the light-receiving side. In this case, probe light froma probe light source 11 is branched into first light and second light.The first light is pulsed by an acoustooptic (AO) modulator 26. At thistime, the probe light is frequency-shifted by an amount of drivefrequency. On the other hand, the second light passes through apolarization controller 27 and is input to a 3-dB coupler 28, disposedon the light-receiving side. Thereafter, the back-scattered light ofidler light from an optical fiber 5 is input to the 3-dB coupler 28through a circulator 15, an optical filter 17, and a polarizationcontroller 28 a. Therefore, the branched light from tap coupler 25 andthe back-scattered light of the idler light are coupled together at the3-dB coupler 28. At this time, the polarization state of the light fromthe tap coupler 25 is caused to coincide with that of the back-scatteredlight of the idler light by the polarization controllers 27, 28 a. Thecoupled light is branched into two light components, which are receivedby a double-balanced-type photodetector 29. An electric signal from thedouble-balanced-type photodetector 29 is amplified by an electricamplifier 30. At a mixer 31, the signal from the amplifier 30 is reducedto a base band by a frequency signal, corresponding to the drivefrequency of the AO modulator 26, output from a signal generator 32. Thesignal from the mixer 31 is fed into an oscilloscope 21 through alow-pass filter 33. The oscilloscope 21 digitizes the input electricsignal and inputs it to a computer 24, which performs a root-mean-squareprocess on the input digital data.

Referring to FIG. 3, there is shown a measurement system 102 constructedin accordance with a third embodiment of the present invention. Themeasurement system 102 is constructed so that by causing third lightdifferent in wavelength from pump light and probe light to enter eitherend or both ends of an optical fiber 5, the powers of pump light, probelight, and idler light are Raman-amplified. Raman amplification isperformed by Raman-amplified light input to both ends of the opticalfiber 5 through two WDM couplers 37 and 38 from two Raman amplificationlight sources 35 and 36. In this case, the WDM coupler 38 may be acirculator. When the wavelengths of pump light and probe light are about1550 nm, light with a wavelength of about 1450 nm is caused to enter theoptical fiber 5. Raman amplification is effective when the fiber lengthof an optical fiber is long and when transmission losses are great.

Referring to FIG. 4, there is shown a measurement system 103 constructedin accordance with a fourth embodiment of the present invention. Themeasurement system 103 is characterized in that it is provided with aoptical spectrum analyzer 39 on the pulse exit side of an optical fiber5. With this optical spectrum analyzer 39, the power P_(c)(z) of idlerlight from the pulse exit end of the optical fiber 5 can be measured.The conversion efficiency G_(c) (=P_(c) (z)/P_(c) (0)) of idler lightcan be calculated from the value of the power P_(c)(z) measured. Ifmeasuring conditions are the same as the aforementioned measuringconditions, the conversion efficiencies in case 1 and case 2 areexpressed by the following Equations:

Case 1: When Δβ<0 (anomalous dispersion) and P_(p)>−Δβ/4 γ,

$\begin{matrix}{G_{c} = {\gamma^{2}{{P_{p}(0)}^{2}\lbrack \frac{\sinh( {g_{a}L} )}{g_{a}} \rbrack}^{2}}} & (28)\end{matrix}$=

Case 2: When Δβ<0 (anomalous dispersion) and P_(p)>−Δβ/4 γ, or when Δβ≧0(normal dispersion),

$\begin{matrix}{{G_{c} = {\gamma^{2}{{P_{p}(0)}^{2}\lbrack \frac{\sin( {g_{b}L} )}{g_{b}} \rbrack}^{2}}}{g_{b} = {\frac{1}{2}\lbrack {{\Delta\beta}( {{\Delta\beta} + {4\gamma\; P_{p}}} )} \rbrack}^{1/2}}} & (29)\end{matrix}$As seen from Eqs. (28) and (29), the conversion efficiency G_(c) ofidler light varies in dependence on the power P_(p) of pump light. Also,A β and γ make a contribution to the variation. Therefore, inexperiments, if a change in the conversion efficiency G_(c) of the idlerlight from the exit end of the optical fiber 5 is calculated as thepower of input pump light is made higher, information on the wavelengthdispersion and nonlinear coefficient of the optical fiber 5 is obtainedin the measured values. Therefore, by making a regression analysis(which employs Eqs. (28) and (29)) when the conditions in the cases 1and 2 are met, two parameters Δβ and γ can be determined. Based on thevalues of Δβ and γ, the average wavelength dispersion and nonlinearcoefficient over the entire length of the optical fiber 5 are obtained.

Typically, there is present polarization mode dispersion in opticalfibers. For that reason, even if the polarization state of pump lightand the polarization state of probe light coincide with each other atthe entrance end of the optical fiber connected to the circulator 15,the two polarization states vary as the pump light and probe lightpropagate through the optical fiber 5. Because of this, when measuringthe optical fiber 5 whose length is long or the optical fiber 5 whosepolarization mode dispersion is great, errors will occur between thepowers P_(c) (z) and P_(s) (z) of idler light and probe light, and thefunctions shown in Eqs. (18), (19), (21) and (22), near the exit end ofthe optical fiber 5. In such a case, one end of the optical fiber 5 isconnected to the circulator 15, and the wavelength-dispersiondistribution and nonlinear-coefficient distribution in the fiberlongitudinal direction are measured. Likewise, the other end of theoptical fiber 5 is connected to the circulator 15, and thewavelength-dispersion distribution and nonlinear-coefficientdistribution in the fiber longitudinal direction are measured. In thisway, pump light and probe light are caused to enter both ends of theoptical fiber 5, like measurements are made, and the two results ofmeasurement are compared with each other. Thus, it becomes possible toselect data where the effects of polarization mode dispersion are less,so the effects of polarization variation on optical fibers can beremoved.

Referring to FIG. 5, there is shown a measurement system 104 constructedin accordance with a fifth embodiment of the present invention. Themeasurement system 104 in the fifth embodiment further includes anonlinear optical medium 40, which is disposed between a coupler 10 forcoupling pulsed pump light and pulsed probe light, and an optical fiber5. As set forth above, when measuring the back-scattered light of idlerlight, the power P_(c)(z) (where z is near zero) of idler light risessharply at the pulse entrance end of the optical fiber 5, so there is agreat error between the measured power P_(c)(z)(where z is near zero)and the solution P_(c)(z)(where z is near zero) obtained by Eqs. (18)and (19). For that reason, the nonlinear optical medium 40 forgenerating weak idler light by nonlinear effects is provided in front ofthe optical fiber 5 so that a light waveform whose error is small isobtained at the light entrance end of the optical fiber 5. As thenonlinear optical medium 40, it is effective to use an optical fiber ofhigh nonlinearity over a short distance.

Referring to FIG. 6, there is shown a measurement system 105 constructedin accordance with a sixth embodiment of the present invention. Themeasurement system 105 is constructed so that in two transmission lines(a first transmission line for pump light consisting of a pump lightsource 1, a phase modulator 2, a power modulator 6, an erbium-dope fiberamplifier 7, a band-pass filter 8, a coupler 10, and a circulator 15,and a second transmission line for probe light consisting of a probelight source 11, a power modulator 12, a delay line 13, the coupler 10,and the circulator 15), the polarization planes of linearly polarizedpump light and linearly polarized probe light become parallel to eachother. Because of this, the phase modulator 2, power modulator 6,erbium-dope fiber amplifier 7, band-pass filter 8, coupler 10, powermodulator 12, delay line 13, and circulator 15 are components having theproperty of holding polarization (particularly, they are represented asa phase modulator 2 a, power modulator 6 a, erbium-dope fiber amplifier7 a, band-pass filter 8 a, coupler 10 a, power modulator 12 a, delayline 13 a, and circulator 15 a). The measurement system 105 furtherincludes optical fiber transmission lines connected between thesecomponents. Thus, pulsed light of two wavelengths is emitted from thepump light source 1 and probe light source 11 so that the twopolarization planes coincide with each other. With the polarizationplanes coinciding with each other, the pump light and probe light arecaused to enter the optical fiber 5. This construction can prevent areduction in the effects of four-wave mixing due to polarizationvariations.

Referring to FIG. 7, there is shown a measurement system 106 constructedin accordance with a seventh embodiment of the present invention. Inaddition to employing an optical heterodyne detection method (see FIG.2) on the light-receiving side, the measurement system 106 isconstructed so that in two transmission lines (a first transmission linefor pump light consisting of a pump light source 1, a phase modulator 2,a power modulator 6, an erbium-dope fiber amplifier 7, a band-passfilter 8, and a coupler 10, and a second transmission line for probelight consisting of a probe light source 11, an AO modulator 26, a delayline 13, the coupler 10 a, an optical fiber 17, a 3-dB coupler 28, a tapcoupler 25, and the circulator 15), the polarization planes of linearlypolarized pump light and linearly polarized probe light become parallelto each other. Because of this, the phase modulator 2, power modulator6, erbium-dope fiber amplifier 7, band-pass filter 8, coupler 10, AOmodulator 26, delay line 13, circulator 15, optical fiber 17, 3-dBcoupler, and tap coupler 25 are components having the property ofholding polarization (particularly, they are represented as a phasemodulator 2 a, power modulator 6 a, erbium-dope fiber amplifier 7 a,band-pass filter 8 a, coupler 10 a, AO modulator 26 a, delay line 13 a,circulator 15 a, optical filter 17 a, 3-dB coupler 28 a, and tap coupler25 a). The measurement system 105 further includes optical fibertransmission lines connected between these components. Therefore, at thelight-receiving part employing the optical heterodyne detection method,the polarization state of pump light and the polarization state of probelight, output from the two pulsed light sources 1 and 11, alwayscoincide with that of the back-scattered light from the optical fibers,so stable reception can be realized.

In the first embodiment, while FFT and IFFT have been employed incalculating g_(b), the present invention is not limited to this. Forexample, the following method may be employed.

By extracting a sequence of data points from data (waveform data)measured by the aforementioned nonlinear OTDR and nonlinearly fittingthe extracted data points to a sinusoidal function, local dispersion canbe calculated. And by changing a range of data to be extracted asoccasion demands and performing the fitting operation,wavelength-dispersion distribution in the fiber longitudinal directioncan be calculated. In FIG. 14 there is shown a waveform having 3743 datapoints in total. For instance, consecutive 201 points near the centerfrom the 1800^(th) point to the 2000^(th) point are extracted. Assumingthe extracted 200 points have a single cycle, a change in the power canbe expressed by the following Eq. (30):F(z,a _(i))=a ₁·sin²(a ₂ ·z+a ₃)+a ₄  (30)Eq. (30) undergoes a nonlinear fitting operation. In this Equation, zand a₂ are parameters regarding position and dispersion, a₁ is anamplitude parameter, a₃ is a phase offset parameter, and a₄ is a poweroffset parameter. These are used as fitting parameters when necessary.

Using parameter a₂, wavelength dispersion can be calculated by thefollowing Eq. (31):

$\begin{matrix}{D = {{- \frac{a_{2}}{\pi\; c}}( \frac{\lambda_{s}}{\Delta\lambda} )^{2}}} & (31)\end{matrix}$The calculated dispersion is assumed to be the dispersion at the centerposition of the above-described range of data extracted (i.e., thedispersion at the 1900^(th) point). The initial value of the parametera₂ employs a cycle obtained by a Fourier transform without a filter, butthe initial value may be a value near dispersion. A method of predictiondoes not matter.

Next, by changing a range of data to be extracted, data points from the1801^(st) point to the 2001^(st) point, for example, are extracted.Similarly, by performing a nonlinear fitting operation, wavelengthdispersion is calculated. The calculated wavelength dispersion isassumed to be the wavelength dispersion at the 1901^(st) point. Afterthe data range is changed, the initial value of parameter a₂ employs theresult of calculation obtained before the data range is changed.Similarly, by changing the data range and performing a nonlinear fittingoperation, local wavelength is calculated. Therefore, the wavelengthdispersion at points in the fiber longitudinal direction is calculated.Thus, the wavelength-dispersion distribution in the fiber longitudinaldirection is obtained. FIG. 15 shows wavelength-dispersion distributioncalculated from the waveform of FIG. 14 by a direct fitting method, thewavelength-dispersion distribution being precisely calculated.

The data range to be extracted may be a suitable range set from thetrade-offs between distance resolution and accuracy. From the nature ofthe fitting operation, the data range to be extracted has sufficientaccuracy when power oscillation is about 1 to 10 cycles.

In addition, Eq. (30) is particularly effective when wavelengthdispersion approximates to a constant in a fitting data range to beextracted, but in the case where wavelength dispersion varies greatly inthe fiber longitudinal direction, it is preferable to employ an equationwhere within a fitting data range to be extracted, wavelength dispersionis distributed in linear dependence on distance. Furthermore, when theamplitude of power oscillation also varies within a fitting data rangeto be extracted, there are cases where the addition of a first-orderparameter for that amplitude is preferred. For first-order parameters,the following Eq. (32) may be employed.

$\begin{matrix}{{F( {z,a_{i},b_{i}} )} = {{\lbrack {a_{1} + {b_{1}z}} \rbrack \cdot {\sin^{2}( {{\lbrack {a_{2} + {\frac{b_{2}}{2}z}} \rbrack \cdot z} + a_{3}} )}} + a_{4}}} & (32)\end{matrix}$in which b₁ represents amplitude and b₂ represents wavelengthdispersion.

Next, a description will be given of a means of correcting forwavelength dispersion calculated from the wave cycle of measured data,by employing the approximate error of an approximate express employed inmeasurement.

The waveform measured by an optical time-domain reflectometer (OTDR) isbased on the assumption that it is expressed by Eq. (30), but Eq. (30)is derived from a differential equation employing the approximation thatidler light generated by FWM is sufficiently small with respect to inputlight. Therefore, the dispersion D, and the parameter a2 about the cycleof the power oscillation of idler light, do not meet Eq. (31) strictly.Particularly, in a system whose nonlinear phenomenon is strong, such aswhen input light is strong and when the nonlinear coefficient of anoptical fiber to be measured are great, the power of idler light isgreat and becomes easy to observe, but approximation errors becomegreat. If wavelength dispersion, calculated by a nonlinear fittingoperation with Eqs. (30) and (31) from power-varied data obtained by asimulation of solving a strict differential equation that haspredetermined wavelength dispersion, is compared with the wavelengthdispersion used in that simulation, the relational expression betweenerrors and parameters is obtained. For instance, assume that the ratioof an input pump light quantity and an input signal light quantity is1:2. And if parameter A is defined by the following Eq. (33):

$\begin{matrix}{{A_{\lbrack{{ps} \cdot {nm}}\rbrack} = \frac{{\Delta\lambda}_{\lbrack{nm}\rbrack}^{2} \cdot D_{\lbrack{{{ps}/{nm}}/{km}}\rbrack}}{\gamma_{\lbrack{{/w}/{km}}\rbrack} \cdot P_{p{\lbrack W\rbrack}}}},} & (33)\end{matrix}$an error in wavelength dispersion becomes

$\begin{matrix}{{Error}_{\;{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack}} \sim {23.80_{\;{\lbrack{{ps}^{2} \cdot {nm}^{2}}\rbrack}} \cdot \frac{\gamma_{\lbrack{\text{/}W\text{/}{km}}\rbrack}^{2} \cdot P_{p\mspace{11mu}\lbrack W\rbrack}^{2}}{{\Delta\lambda}_{\lbrack{nm}\rbrack}^{4} \cdot D_{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack}}}} & (34)\end{matrix}$when the value of A is 10 or more. An error between the true value ofwavelength dispersion and the value of wavelength dispersion calculatedfrom the waveform measured by an optical time-domain reflectometer(OTDR) is calculated by Eq. (34). Therefore, by calculating an errorfrom a measured value and compensating for the calculated error, itbecomes possible to calculate the true value of wavelength dispersion.

For example, if an optical fiber with a wavelength dispersion of 2.00ps/nm/km and a nonlinear coefficient of γ=2.025/km/w is measured withthe conditions the power of input pump light is P_(p)=200 mW, the powerof input signal light is P_(s)=400 mW, and that the wavelength spacingbetween the input pump light and the input signal light is 2.298 nm, anerror is 0.07 ps/nm/km. That is, if wavelength dispersion is calculatedfrom a measured waveform by Eqs. (30) and (31), it is 2.07 ps/nm/km.Therefore, when measured wavelength dispersion is 2.07 ps/nm/km, anaccurate value of 2.00 ps/nm/km can be calculated by subtracting anerror of 0.07 ps/nm/km from the measured value 2.07 ps/nm/km containingthat error.

In Eq. (34), an error in wavelength dispersion can be calculated fromthe above-described nonlinear coefficient, input pump light power, inputsignal light power, and spacing between the wavelength of the input pumplight and input signal light, but if P_(c) represents the wave amplitudeof idler light when a Rayleigh scattering coefficient is 10⁻⁴, and fiberloss is assumed to be zero, the above-described error can be expressedas:

$\begin{matrix}{{Error}_{\;{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack}} \sim {1.94 \times {10_{\lbrack{{ps}^{\frac{2}{3}} \cdot {nm}^{\frac{2}{3}}}\rbrack}^{3} \cdot D_{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack} \cdot ( \frac{\gamma_{\lbrack{\text{/}W\text{/}{km}}\rbrack} \cdot P_{c\mspace{11mu}\lbrack W\rbrack}}{D_{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack} \cdot {\Delta\lambda}_{\lbrack{nm}\rbrack}^{2}} )^{\frac{2}{3}}}}} & (35) \\{{Error}_{\;{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack}} \sim {1.83 \times {10^{4} \cdot D_{\lbrack{{ps}\text{/}{nm}\text{/}{km}}\rbrack} \cdot \frac{P_{c\mspace{11mu}\lbrack W\}}}{P_{p\mspace{11mu}\lbrack W\rbrack}}}}} & (36)\end{matrix}$Because of this, a compensation for an error in measured wavelengthdispersion can be made by employing the nonlinear coefficient, theobserved wave amplitude of idler light, and the wavelength spacing ofthe two inputs. In addition, a compensation for an error in measuredwavelength dispersion can be made by only the input pump light power andobserved wave amplitude of idler light. Particularly, if Eq. (36) isemployed, a compensation for an error can be made without calculating anonlinear coefficient, so it is useful. That is, if Eq. (36) isemployed, the wave amplitude of idler light is 4×10−4 mW with the samemeasuring conditions as the aforementioned conditions, so an error of0.07 ps/nm/km can be calculated with the wave amplitude of input pumplight P_(p)=200 mW when wavelength dispersion is 2.00 ps/nm/km, withoutemploying a nonlinear coefficient in the calculation.

Conversely, in the case where the ratio of the light quantity of inputpump light and the light quantity of input signal light is 1:2, whenmeasuring the wavelength dispersion of an optical fiber in which thewavelength dispersion is 2.00 ps/nm/km and the nonlinear coefficient isγ=2.025/km/W, it is found that if the wavelength spacing is made great,or if the wave amplitude of input pump light is made small, an errorbecomes smaller. An approximation error is inversely proportional to thefourth power of wavelength spacing and is proportional to the square ofthe power of input pump light. However, since idler light becomes smallin proportion to the square of input pump light power, the waveamplitude of input pump light is determined within a range where idlerlight is measurable.

Therefore, in order to calculate the cycle of local power oscillation ofmeasured data, by directly performing a nonlinear fitting operation witha sinusoidal function, the influence of noise can be removed andaccuracy of analysis can be enhanced. In addition, the analysis ofdirectly performing a nonlinear fitting operation makes a filter processunnecessary and is easy to handle, so analysis becomes easy. Acompensation for an approximate error is made by inverse operation, soit becomes possible to increase accuracy of analysis. Moreover, becausemeasurement errors can be made small by selecting assumed conditionswhere an approximation error is small, accuracy of measurement isenhanced.

While the present invention has been described with reference to thepreferred embodiments thereof, the invention is not to be limited to thedetails given herein, but may be modified within the scope of theinvention hereinafter claimed.

1. A method of measuring wavelength-dispersion distribution in alongitudinal direction of an optical fiber to be measured, comprising:generating pulsed probe light linearly polarized, and pulsed pump lightthat is different in a wavelength from said probe light but has the samepolarization state; causing said pulsed probe light and said pulsed pumplight to enter an optical fiber to be measured; extracting waveform dataincluding a power variation of back-scattered light of idler lightgenerated by four-wave mixing within said optical fiber, for each of aplurality of regions; nonlinearly fitting said waveform data extractedfor said regions to a sinusoidal function expressing said powervariation of said back-scattered light; respectively calculatingdispersions of said waveform data extracted for said regions; andmeasuring said wavelength-dispersion distribution.
 2. The measurementmethod as set forth in claim 1, wherein assuming the extractedconsecutive plural points have a single cycle for each of said regions,said sinusoidal function is expressed by the following Equation whichexpresses said power variation (a change in the power) for each of saidregions:F(z,a _(i))=a ₁·sin²(a ₂ ·z+a ₃)+a ₄ where z and a₂ are parametersregarding position and dispersion, respectively, a₁ is an amplitudeparameter, a₃ is a phase offset parameter, and a₄ is a power offsetparameter.
 3. The measurement method as set forth in claim 1, wherein ina case where wavelength dispersion varies greatly in a longitudinaldirection of said optical fiber, said sinusoidal function is expressedby the Equation where said wavelength dispersion is distributed inlinear dependence on distance, for each of said regions.
 4. Themeasurement method as set forth in claim 3, wherein in a case where anamplitude of power oscillation varies for each of said regions, saidsinusoidal function is expressed by the following Equation whichexpresses said power variation for each of said regions:${F( {z,a_{1},b_{1}} )} = {{\lbrack {a_{1} + {b_{1}z}} \rbrack \cdot {\sin^{2}( {{\lbrack {a_{2} + {\frac{b_{2}}{2}z}} \rbrack \cdot z} + a_{3}} )}} + a_{4}}$where z and a₂ are parameters regarding position and dispersion,respectively, a₁ is an amplitude parameter, a₃ is a phase offsetparameter, a₄ is a power offset parameter, b₁ represents said amplitudeand b₂ represents said wavelength dispersion.
 5. The measurement methodas set forth in claim 1, wherein from the nature of the fittingoperation, the data range to be extracted has a plurality of cycles.